We have studied the spacetime of a Kerr black hole immersed in Melvin magnetic field, and found Melvin-Kerr black hole shadow becomes more elongated as the magnetic field parameter $B$ increases. We found not only that an unstable light ring could exist but also that a stable light ring could exist. The unstable light ring radius increases with the increase of $B$, but it is the opposite for a stable light ring. For a certain rotation parameter $a$, both the prograde and retrograde unstable (stable) light rings exist when $B$ is less than a critical value $B_c$ for retrograde light ring. In this case, the shadows of Melvin-Kerr black hole have two regions corresponding to the prograde and retrograde stable photon orbits on both sides of the middle main shadow. As $B$ continues to increase, there is only the prograde unstable (stable) light ring. In this case, the region corresponding to the prograde stable photon orbits emerges in the life of the main shadow. The absence of the retrograde unstable (stable) light ring makes the Melvin-Kerr black hole shadow a half-panoramic (equatorial) shadow. When $B$ is bigger than $B_c$ for a prograde light ring, neither the prograde nor retrograde unstable (stable) light ring exists. In this case, the shadow of Melvin-Kerr black hole becomes a panoramic (equatorial) shadow. In addition, there also exist some self-similar fractal structures in the shadow of Melvin-Kerr black hole arising from the chaotic motion of photon.

• Received 15 May 2021
• Revised 24 August 2021
• Accepted 7 September 2021

DOI:https://doi.org/10.1103/PhysRevD.104.084021